<p>In this thesis, Robust Slepian-Wolf coding problem is discussed. Two correlated source sequences Xⁿ and Yⁿ are encoded at separate encoders and decoded together. When the encoder of source Y is broken, another sequence Xⁿ still can be decoded to achieve a nontrivial distortion. Further, Xⁿ can be recovered losslessly once that broken encoder is restored. A practical coding scheme is developed using low density graph codes. Moreover, by generalizing the coding scheme of Robust Slepian-Wolf coding problem, two approaches are proposed for the Wyner-Ziv problem using the low density graph codes.</p>